Amy Schumer photographed at the Soho hotel in London. Photograph: Pal Hansen for the Observer

There are two bottles of mineral water in Amy Schumer’s hotel suite and no glasses. She takes sparkling, I have the still, and I offer to find something to drink out of. “Naaah, let’s drink it out of the bottle,” Schumer, the 34-year-old American comedian and actor, suggests. She slumps on the sofa, tucks her feet underneath her and takes a thirsty swig. She’s just come from doing photographs and is wearing an expensive-looking peach cocktail dress; her hair and nails are done. The effect is incongruous: she looks like a girl whose prom date has stood her up.

Nice dress, I say – mainly because that kind of clothing and conspicuous effort demand acknowledgement. It turns out to be not Schumer’s choice and certainly not her taste. “Does this look hilarious, this orange thing?” she asks. “I feel like the exact opposite of this outfit and nail polish. I feel no connection to how I look visually right now.”

What outfit should she be wearing? “All grey, no makeup.” Why, is today a grey day? “Oh no,” Schumer corrects, “That’s every day. I wish I was dressed like a rainy cloud.”

Life is actually not so bad for Schumer. We meet on a Thursday afternoon in early June and she has won three awards in that week alone. The previous Sunday, sketch show Inside Amy Schumer was honoured in New York at the 74th Peabody awards, which reward excellence in broadcasting; 30 Rock’s Tina Fey introduced her and suggested they might share a “very awkward, staged lesbian kiss” so that Fey could “feed off her youth”. Schumer came to the stage and, bullied by the audience, they did exactly that, slightly awkwardly. Back at her table, she discovered from a phone message that she had just won best actress in a comedy series at the Critics’ Choice Television awards in Los Angeles, too.

The night before our interview, now in London, Schumer gave a near-six-minute acceptance speech for winning the trailblazer of the year title at the 2015 Glamour Women of the Year awards. With Jennifer Saunders standing behind her – “It’s the funniest fucking stuff you will ever, ever see,” Saunders had said in a rambling preamble – Schumer’s monologue covered the usual: having her first period, her relief at not having to pose with a plastic dick in the magazine’s photographs, before signing off with an empowering message of not apologising for who you are and loving the skin you’re in. The footage has been watched more than 3m times on YouTube. (It’s not a competition, but – if you’re thinking, “Well, I’ve never heard of her…” – Caitlin Moran’s speech at the same awards has had around 5,000 views.)

Schumer is in Britain to promote the new movie Trainwreck, which she wrote and stars in. It came about after the director Judd Apatow (The 40-Year-Old Virgin, Knocked Up) heard a radio interview with her while he was sitting in his car. She talked about shoplifting as a child, her first encounter with an uncircumcised penis and dealing with her father’s multiple sclerosis. “I was blown away by how funny and intimate and fresh she was,” Apatow remembers in his new book, Sick in the Head: Conversations About Life and Comedy. “You could sense that she had stories to tell and was a lot more than just a comedian. I instantly thought: I need to make a movie with her.”

In the first script Schumer sent Apatow, her character was a used-car saleswoman. Apatow wasn’t convinced and asked her to write something more personal. And that’s what he got: Trainwreck is the story of a woman named Amy who lives in New York and has chaotic family relationships and a self-destructive approach to dating. She drinks too much and hops from bed to bed before meeting a wry, funny surgeon called Aaron (Saturday Night Live’s Bill Hader), whom she finds harder to discard than usual.

Amy Schumer’s acceptance speech at the 2015 Glamour Women of the Year awards.

“It’s a very personal story,” says Schumer. “I wrote it two years ago and it’s kind of about myself, a version of myself, like maybe from a younger age.” Her voice, a significant part of her comedic success, managing simultaneously to convey both innocent sweetness and world-weary sarcasm, now leans more towards the latter. “I would say it’s 48% autobiographical.”

The interview, I won’t lie, is a little cranky at this point, and for much of the first 20 minutes. Lots of dead ends, frequent misunderstandings, uncomfortable pauses. Answering questions she’s no doubt heard before probably has something to do with it, but it feels more atmospheric: the setting, her clothes, maybe even the pressure of promoting a $35m (£22m) film that most people are expecting to be very good. She’s not done a press junket before: endless hours of deluxe house arrest while international writers file relentlessly in and out. Eventually, Schumer concedes as much.

“This is my first time doing it, but it’s just so ridiculous,” she says. “I don’t want to dress like a dickhead and talk about myself. A lot of it feels like I’m being punished for doing something that I’m proud of. Imagine all day having to talk about your writing. Wouldn’t you just run a warm bath and open your wrists?”

I think I’d quite like it, I reply. Schumer snorts: “Bullshit!” And we get along better after that.

There are two main reasons that people are freaking out, especially in America, more and more in Britain, about Amy Schumer. The first is that she is extremely funny. Her humour is often oversharing exhibitionism, deriving from that repository we all have of “things you’re ashamed of but will never tell another living soul”. There’s a scene in Trainwreck where Schumer attends her sister’s baby shower. The other women, mostly pristine and uptight, share their darkest secrets – one, for example, is ashamed of letting her children watch Glee – before Schumer details how, after particularly vigorous sex, the condom became attached to her cervix and she had to fish-hook it out with her finger.

Perhaps inevitably, this is an experience that really did happen to Schumer, the baby shower part, anyway. The story she actually told – as she detailed in her 2012 standup special Amy Schumer: Mostly Sex Stuff – was far more explicit and embarrassing: it involves a drunken sex act with a New York taxi driver while her friend slept in the back when Schumer was in her early 20s. The truth, it turns out, can be stranger than fiction.

Schumer – who, in person, is much less extrovert – appears immune to embarrassment as a performer. In April, she was named in Time’s 100 Most Influential People list; the actor Tilda Swinton wrote, in her endorsement: “She’s an honesty bomb. Coming to get you.” At the red carpet before the Time gala in New York, Schumer noticed Kanye West and Kim Kardashian in front of her and took a dramatic pratfall to land at their feet. Everyone got the joke, except Kanye perhaps, who didn’t crack a smile. “There’s no way that either of them had any idea who I am,” Schumer said afterwards. “So that was comforting.”

The second reason Schumer seems especially important at the moment is that she has become a powerful feminist voice. This became clear with a speech she gave at the 2014 Gloria awards, organised by women’s rights activist Gloria Steinem to celebrate “women of vision”. This, too, started from an awkward personal revelation – a one-morning stand she had in college (he called her, still drunk, after a long, heavy night) that she later realised came from plummeting self-esteem about her looks – but it also had an inspiring, rallying take-home power. It’s worth tracking down to read in full, but she concluded: “I stand here and I am amazing, for you. Not because of you. I am not who I sleep with. I am not my weight. I am not my mother. I am myself. And I am all of you, and I thank you.”

“It’s just who I am,” says Schumer, when I ask if she set out with a specific feminist agenda. “So it happened naturally, just being myself. I think feminists are in good hands with me.”

More subliminally powerful – it’s been called “sneaky feminism” – are the sketches from Inside Amy Schumer, which recently finished its third series in America, and can be tracked down at odd hours on Comedy Central in Britain. The most ambitious of these was an episode-long parody of 12 Angry Men where the jurors – Paul Giamatti, Jeff Goldblum and Mad Men’s Vincent Kartheiser among them – have a furious back-and-forth about whether Schumer is “hot enough to be on TV”. Lena Dunham, the creator of Girls, recently described it as “the most important thing that’s happened on TV in a long time”.

In another rightly revered sketch, Schumer happens upon Julia Louis-Dreyfus, Patricia Arquette and Tina Fey by a river having a picnic. They are celebrating Julia’s “last fuckable day” – a media construct whereby female actors are no longer considered believable as a love interest in films – before giving her a Viking send-off. “I know the movies I’ve seen and I’ve heard friends,” says Schumer. “Maggie Gyllenhaal being told that it’s not believable that a 60-year-old would want to fuck you. It’s a glaring oddity in movies to say: Steve Carell and Keira Knightley, yeah. Or Jack Nicholson and Amanda Peet, of course. It’s annoying. I don’t even know if it’s that unrealistic, though.

“But, for me, I’m not either of those girls. I’m not going to get any roles because like: ‘Well, who’s the hottest person for this job?’”

Does Schumer feel part of a movement with Fey, Dunham and others? “No,” she replies, her response perhaps triggered by the inane line of inquiry. “I’ve never thought of that before, but it sounds good, though. I’d love to be part of a movement. I feel very connected to people like Tina or Lena because it feels like we have the same goal in mind.”

Schumer is quick to note that overt sexism is found in many other places besides entertainment. Moreover, it’s not just that there’s an “aggression” – her word – from men towards women, but also from women towards women. “Pick a scenario,” she says. “It’s like the reason people hate Hillary Clinton. I really like her. But she made a lot of women mad because she wasn’t baking Christmas cookies and she made a lot of men mad and they don’t even know why. I think it’s because she triggers something in them; them being yelled at by their mom or something. I do think there’s an aggression from a lot of men. Like a lot of men just want to know that you would fuck them or they can’t be calm around you. That they would have the option to have sex with you.

“Any executive who’s at the head or whatever of their business, if they’re a woman, they’ve had to figure out what hat they need to put on,” Schumer continues. “This guy needs me to be maternal to him; this guy needs to think I would have sex with him; this guy needs me to have sex with him; this girl needs to know that I’m lonely – in a way that I don’t think is required from men.”

Inside Amy Schumer began life as a “secret feminist idea”, she says, but with its success – which, admittedly, is predominantly with critics and on YouTube, rather than in ratings – it can afford to be more overt. In the most recent series, in another parody – this time of Friday Night Lights, the US television drama set in small-town Texas – an American football coach arrives at a new high school and attempts to introduce a “no raping” rule with his team. His players are bewildered, then angry: “What if the girl said yes to me the other day, but it was about something else?” one asks. Schumer has often reiterated that there’s almost nothing she won’t make a joke about – so long as it feels true and makes people laugh – and she’s made clear that she really means it.

“People get really turned off by feminism,” she says. “Nobody wants to feel they’re learning anything and we’re on an 18 to 34, male-dominated network, so we kind of had to trick people into watching. Someone said that our show is the equivalent of putting shaved carrots into brownies and I really like that.”

If Trainwreck is indeed 48% autobiography, it’s easy to get muddled in the crossover between the two Amys. Schumer, the real-world one, was born in Manhattan and has an older brother, Jason, and a younger sister, Kim. Gordon, her father, sold upmarket baby furniture imported from Italy until, in short order – when Schumer turned 12 – he was diagnosed with multiple sclerosis and his company went bankrupt. The family moved out to Long Island and her parents divorced. This period, Schumer believes, is where her humour really coalesced: nothing was so dark or painful that it couldn’t be undercut by laughing really hard about it.

In Trainwreck, Amy’s father is also called Gordon (played by Colin Quinn), has MS and lives in a nursing home. The scenes between the two of them are intensely moving but also uncomfortably vivid. “My dad’s seen the movie and he loves that I’ve wrote my mom as being dead, which she’s not,” says Schumer. “My dad is just like Colin in the movie, he really is, he’s a total wise-ass sarcastic, still tries to get laid even though he lives in a hospital and he’s in a wheelchair. He loves me so much, but once in a while he can be a little harsh. That’s similar to real life. Those scenes are pretty close to reality.”

Trainwreck Amy also has a sister called Kim (Brie Larson), but she, and their acrimonious relationship, is more of a creation. As children, Kim (the real one) was her sidekick and it was to Schumer’s great disappointment that she got married, moved to Chicago and became a school clinical psychologist: “I was like, ‘Look, whenever you’re done with this charade…’” When her sketch show earned a second season, Schumer persuaded Kim to move to New York and join the writing team; she’s also a producer on Trainwreck.

“I’m insanely close to my sister,” says Schumer. “She lives six blocks from me and she and her husband wear pyjamas with footies on them” – onesies essentially – “and just play with their dog. I love hanging out with them the most. I was like, I could stay in London another couple of days and see this very cool, beautiful city, but I think I’d rather just go home and watch TV at their house.” Schumer once posted a video of her serenading the dog on the sofa and gave it the caption: “Boyfriend.”

In Trainwreck, Amy is a writer at a men’s magazine called S’Nuff. It’s a place where staffers pitch articles such as “You’re not gay, she’s boring” and “Ugliest celebrity kids under six”. The contempt, Schumer reveals, is genuine. “Some men’s magazines are just downright offensive,” she says. “They parody themselves: the coverlines I was writing were not as ridiculous as the ones in real life. My experience is that 5% of the issue is stuff you could be really proud of and say: ‘But look, we’re doing this!’ The rest of it – and this is entertainment in general – is to make money, appeal to the attention-deficit times we’re living in and play on people’s insecurities. Anybody who works in those environments, to some extent, has to justify, ‘How am I going to be able to sleep at night?’”

Again, though, Schumer is not just pointing the finger at men. The editor of S’Nuff is a woman, Dianna (Tilda Swinton), and she is the meanest and most amoral of everyone. It is on her orders that Amy, who thinks “sports are stupid”, is assigned to profile Aaron, a surgeon who specialises in sports injury and whose clients include basketball star LeBron James. As part of her pep talk, Dianna tells her: “I like you, Amy. You’re clever, but you’re not too brainy. You’re prettyish, but you’re not too gorgeous. You’re approachable.”

For Schumer – whose 12 Angry Men sketch was a half-hour of far more lacerating personal insults – such self-deprecation is expected. In a conversation with Schumer for his book Sick in the Head, Apatow sums it up this way: “You’re in a weird area. I would describe it as: everyone thinks you are beautiful, but maybe you don’t agree with their opinion.”

So is that how Schumer feels about herself: “approachable”? Where does that estimation come from? “Life,” she shoots back. “What did you think? Did you think I was better-looking than that or less attractive?”

I’m not sure what the right answer is; neither seems likely to end well. I instead suggest, doesn’t everyone secretly think they are better-looking than they are? “You think?” Schumer replies. “That’s so nice. Do you have kids? You should. That’s such a great mentality. No, I think most people hate themselves.”

Schumer’s on a roll now. “That’s such a male thing,” she goes on. “I have a joke where I say, girls, we’re all like, ‘Maybe I’m gorgeous and I just don’t know it.’ But really most girls are like, ‘Oh God, I’m not!’ Even the most beautiful think they’re disgusting.” She pauses, collects her thoughts. “I feel sexy. I feel good. But if I’m in a bar and you just look over and see me? You’d be like,” she shrugs her shoulders, unimpressed: “Ehhhh…”

Schumer plans for this to be an ongoing relationship with Apatow. “I think I’ll make another movie with Judd for sure,” she says. “I wouldn’t have written this movie if he didn’t encourage me to write it. I didn’t write it and find a director. I was just afraid I’d lose a hold of it and the story of my character wouldn’t be portrayed the way I wanted her to be. That never happened – but that was a fear of mine that wasn’t gone until the final cut was delivered and I really love the movie.”

So, no tantrums or bust-ups on set then? “Oh my God, Judd’s the most sweetest, passive dude,” says Schumer. “Like the most devout husband and father you could imagine. Does not check out an ass going by – I think he’d die before he did that. I would say pretty asexual, the sex scenes were definitely worse for him than for me. Yeah, like a teddy bear with a penis.”

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Schumer is at an odd stage at the moment. Objectively, her career couldn’t be going much better, and she knows that. Inside Amy Schumer was immediately recommissioned for a fourth series. She recently recorded a standup special for HBO – the ultimate validation for a US comedian – and Chris Rock agreed to direct it. Trainwreck made $30.2m on its opening weekend in the US, making it an instant hit; the audience was two-thirds female and more than a quarter went specifically because of Schumer. “That is star power, plain and simple,” wrote Scott Mendelson in Forbes. Anne Hathaway – the butt of one of the film’s jokes – suggested in a somewhat queasy Instagram post that Schumer could expect Oscar attention for writing and acting.

“Yeah, I never dreamed of this,” says Schumer. “My dreams were like, ‘Maybe I could work in a cool dinner theatre… Could I play Tina in Tony ’n Tina’s Wedding?’ This was beyond my dreams.”

Offers are tumbling in. Schumer turned down replacing Jon Stewart as the host of The Daily Show, because she didn’t want to know what she would be doing for the next five years. She has mostly completed a book of autobiographical essays. With her sister, she has just finished rewriting an original script by Katie Dippold, whose credits include The Heat, the 2013 hit starring Melissa McCarthy and Sandra Bullock, and the forthcoming all-female Ghostbusters reboot. The script is said to be an action comedy about a mother and daughter on holiday and Paul Feig, who directed Bridesmaids and The Heat, is signed on as a producer. “It’s the only script I’ve read that I really responded to,” says Schumer. There’s speculation that she might even direct it.

“Because I have standup in my life, I have the freedom not to say, ‘Yeah, I’ll be the stupid friend who has no substance and doesn’t evolve at all.’ I can say, ‘No, I don’t want to be Olivia Wilde’s fat friend.’”

Schumer pretends to trip and fall on the floor in front of Kim Kardashian and Kanye West at the Time 100 Gala in New York. Photograph: Getty

At the same time, though, Schumer knows she is due a backlash. She thinks she maybe has a couple of months. There are rumblings already, notably an article in the Guardian by Monica Heisey in June that, while praising much of Schumer’s work, claimed she has “a shockingly large blind spot around race”. Heisey cited standup lines such as, “Nothing works 100% of the time, except Mexicans.” Schumer defended herself vigorously, noting that part of her comedy is to adopt the persona of “an irreverent idiot … who time to time says the dumbest thing possible.” Playing with ideas of race is something comedians should do, she argued in a statement. “I ask you to resist the urge to pick me apart. Trust me. I am not a racist… So move on to the next person who is more deserving of your scrutiny and not the girl in your corner.”

Even if she’s nixed that controversy for now, Schumer expects there to be more. She plans to be vocal in her support of Clinton in next year’s presidential election and she knows that won’t be universally popular. “I hope she’ll win,” she says. “I just haven’t seen any candidate yet that’s anywhere near as qualified.”

Our time is running out. There is, doubtless, another journalist outside wanting her to talk more about herself. Has Schumer’s recent success at least made her happier? “I’m happier because I have more money,” she answers. “I’ve been able to give my brother and sister money, so we’re taken care of. But I’m exactly as happy as I was when I was waiting tables. I don’t think people get happier. But knowing that you’re financially OK and you can have health insurance is really nice. And I get to do cool things. But yeah, I think I’m the same amount of happy.”

Schumer remains determinedly a rainy cloud, even in a week in which she has won three awards. I remind her of this. “Oh my God, I did win three awards this week,” she says, doing a convincing impersonation of someone who might have forgotten that. “And I also found my grill [tooth jewellery]. I couldn’t find my grill that I had made for a shoot” – it fitted over her lower teeth and spelt “Bo$$” in sparkly lettering – “and I just found it in a purse. So it’s a pretty good week.”

Eventually, Schumer does admit that she has been affected by the response she’s provoking. Especially the Peabody award, where other winners included CNN’s coverage of the kidnapped Nigerian schoolgirls. “We made this little show and now we’re getting an award next to people who were trying to rescue 200 girls from sexual slavery,” says Schumer. “I feel preposterous. Like, why am I allowed to be in the room with you guys? And they’re coming up: ‘Can we have a picture with you?’ You want a picture with me? I’m like, ‘This is humiliating.’”